Your drawing is correct. The path of the Sun in the sky is a circle, but it’s not necessarily a great circle (only on the equinoces). From April to August, the Sun is north of the “Celestial equator”, and from October to February, it’s south of the celestial equator (this is the cause of the seasons). How much the Sun varies from the equator depends on the Earth’s inclination, but that’s not really important here. The angle between the plane of the circle and the plane of the ellipse (presumably horizontal) is determined entirely by your latitude: The angle should be 90 degrees minus your lat. So at the North Pole, the circle would be flat; at the equator, it would be standing on its edge, and at the Montana-Wyoming border, it would be tilted up halfway between horizontal and vertical.
Mogadon, I agree there are many reasons to have the base 60 or base 12 number system. More than there are reasons not to, really. But it is only in time and the geometry of circles it has survived. My point is that this is because it is immensely difficult to use a base 10 system with circles. How the Babylonians divided the circle into 60 subunits is beyond me. Especially without Pythagoras to lend a hand. But maybe they weren’t big on precision, in which case the entire discussion is futile.
Chronos: The angle between the plane of the elipse and the plane of the circle would be 90 degrees minus your lat, minus the earths inclination at the time of year, so it is not entirely irrelevant.
ras2000,
I am just jumping into this discussion without too much knowledge of what the critical issues you are talking about are - reading earlier posts you seem to be addressing several things! Pardon my ignorance if my remarks are pointless!
1 - I think that Mentock has pointed out that the circle probably wasn’t the main reason for the base60 measurement - it was just used because that was standard measurement for the time.
2 - I am not sure that “…they survived all these years. After all the base 60 number system died a silent death everywhere else.” gives an balanced view of the use of base10 measurement. After all, base10 is surely fairly recent? I used base12 and base20 for money until 30 years ago. When would you say base10 became popular? 150 years ago? Not a long time - it may just be a flash in the pan!
3 - There seems to be an idea that hours and minutes have to be equal lengths of time - I think that this is a comparatively modern idea as well. Perhaps Chronos can enlighten me? I seem to remember that in the early days of mechanical timekeeping quite a lot of effort was expended making the hours longer in the summer and shorter in the winter, so 12 would fit in a day? I suppose astronomy needed time measurement before railways, but even so, we are only talking a few hundred years - a thousand at most?
4 - I think the ancients were quite big on precision - by being quite big. Didn’t Tycho Brahe have a 100ft or so astrolabe?
ras2000,
I am just jumping into this discussion without too much knowledge of what the critical issues you are talking about are - reading earlier posts you seem to be addressing several things! Pardon my ignorance if my remarks are pointless!
1 - I think that Mentock has pointed out that the circle probably wasn’t the main reason for the base60 measurement - it was just used because that was standard measurement for the time.
2 - I am not sure that “…they survived all these years. After all the base 60 number system died a silent death everywhere else.” gives an balanced view of the use of base10 measurement. After all, base10 is surely fairly recent? I used base12 and base20 for money until 30 years ago. When would you say base10 became popular? 150 years ago? Not a long time - it may just be a flash in the pan!
3 - There seems to be an idea that hours and minutes have to be equal lengths of time - I think that this is a comparatively modern idea as well. Perhaps Chronos can enlighten me? I seem to remember that in the early days of mechanical timekeeping quite a lot of effort was expended making the hours longer in the summer and shorter in the winter, so 12 would fit in a day? I suppose astronomy needed time measurement before railways, but even so, we are only talking a few hundred years - a thousand at most?
4 - I think the ancients were quite big on precision - by being quite big. Didn’t Tycho Brahe have a 100ft or so astrolabe?
Base 10 is a lot older than 150 years. Yes, some units were and are based on other numbers, but the number system itself is based on ten, and has been for millenia. Of course, our modern place-value system is base ten, but so were the Roman and Greek systems before that: X is ten, C is a hundred, and M is a thousand, but there’s no special symbol for twelve, twenty, or sixty.
As for hours, I’m pretty sure that you’re correct, that an hour was one twelfth of the time from sunup to sundown (or sundown to sunup, at night). But on any given day, each hour was (nominally) the same length (to the precision they had available, at least: Tycho had insane precision, but he wasn’t exactly an “ancient”.). I’d never heard that the builders of the first mechanical clocks tried to match them to the “exactly 12 hours of light” standard, though.
Before you ask any more questions, by the way, as a student of physics, and particularly relativity, I can claim to be somewhat of an expert on time, but I can claim no such expertise on the history of human methods of timekeeping. Most of what I know on the subject comes from fuzzy memories of Latin classes a decade or more ago.
What I know about time is pretty much what is written in this thread, and most of it has been news to me. I’m just very interested in geometry, and I always thought that the 12 hours stayed with us because it was so much simpler that way. But I may be way off.
posting in a hurry:
Googling on Helios, cattle, 360 and such there are references to a 360 day calendar used by Egyptians, Mayans, Greeks and such. The guys in the Odyssey got in trouble with the sun god, Helios, by eating some of his 360 cattle, thus screwing up the year.
Someway that I don’t visualize, a shadow or a star or something, moves 1/360 of a circle because the earth has moved that much around the sun. Maybe this is the reason for the base 360 numbering system.
From an external point of view, the Earth moves about a degree a day in its orbit around the Sun (there’s 365.25 days in a year, not 360, but 360 is a nicer number mathematically, so most ancient cultures fudged the extra 5+ days). From an Earthly perspective, that translates to the Sun moving a degree a day, relative to the stars. This might not seem an obvious thing to measure, since you can’t see the Sun and the stars at the same time. But you can check things like what star is directly overhead at midnight, or when in the year a star is first just barely visible before dawn. This latter is called the “heliacal rising” of the star, and happens at the same date every year (if your stargazers are alert and looking for it). The heliacal rising of Sirius comes just before the Nile’s seasonal floods, so that one in particular was important to the Egyptians (of course, they supposed there was a causal connection). The point is, they saw that something was changing by about a degree each day.
Sorry for the slight hijack, but this question was just asked me, and having an expert on the boards…
Dusting off my memory of college Astronomy and physics, I recall the movement of the earth by ~1 degree in orbit accounted for the idfference between Greenwich Standard Time (GST) and Sidereal Time (ST), right? GSTT being the current time at Greenwich, England, and ST being the amount time since the Vernal Equinox was directly overhead (at the zenith). As a result Sidereal Time could differ by as much as plus/minus twelve hours compared to GST. Each day, then, ST moves by about 4 minutes. Am I right in this, or am I just muddying the waters?
Yes. Imagine that the Earth went around the Sun the way the Moon goes around the Earth. In that case, there would be zero solar days in the year, but one sidereal day. In fact, there are about 365.22 solar days per year, and 366.22 sidereal days per year.
Level3Navigator, you’re basically correct about sidereal time, but one should also add that there’s “local sidereal time”, in much the same way that there’re different time zones for sun time. Except that astronomers usually need more precision than an hour, so local sidereal time is a continuous function of longitude, not a discrete function like time zones (so a person a little bit west or east of me will have a different sidereal time, even though we probably both have the same clock time). So it’s perhaps a bit misleading to compare sidereal time with GMT.
Though I understand the point you make about the divisibility of a circle, I don’t think there aren’t 12 lunar evolutions per year every year… some years, there are 13.
Also, the number 12 might have some significance because it is a multiple of three, which was a sacred number, given that there are three sacred realms, and all that.
